Check force on energy

It is common practise to use the potential energy as a collective energy. Some MD codes thus pass the potential energy to PLUMED and PLUMED can then apply forces on this collective variable. We test that any forces that PLUMED applies on the potential energy are correctly passed back to the MD code by doing the following test. We first run a short simulation at $T$ K with a timestep of $\tau$ ps. During the course of this simulation we monitor the potential energy using the following PLUMED input:

Click on the labels of the actions for more information on what each action computes
tested on2.10
tested onmaster
e: ENERGYCalculate the total potential energy of the simulation box. More details
v: VOLUMECalculate the volume the simulation box. More details
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=e,v FILEthe name of the file on which to output these quantities=energy1

We then run a second simulation (starting from identical conditions) at a temperature of $T\alpha$ and with a timestep of $\tau/\sqrt(\alpha)$. The thermostat and barostat relaxation times are similarly divided by $\sqrt(\alpha)$. In the tests that are run on this website we set $\sqrt(\alpha)=1.1$. The PLUMED file above is used when this test is run but a different time series of energy values is recorded as the MD parameters in this second simulation are different.

If PLUMED is working correctly we should be able to recapture the time series of energy values for the first simulation by running an MD simulation with the modified parameters that were used in the second simulation and the following PLUMED input file:

Click on the labels of the actions for more information on what each action computes
tested on2.10
tested onmaster
e: ENERGYCalculate the total potential energy of the simulation box. More details
v: VOLUMECalculate the volume the simulation box. More details
# slope is such that 
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=e FILEthe name of the file on which to output these quantities=energy2
# slope should be (alpha-1)=0.21
RESTRAINTAdds harmonic and/or linear restraints on one or more variables. More details ATthe position of the restraint=0.0 ARGthe values the harmonic restraint acts upon=e SLOPE specifies that the restraint is linear and what the values of the force constants on each of the variables are=0.21

In other words, when forces are passed correctly the time series for the energies and volumes from the first and third of these calculations should be identical.

To determine if PLUMED passes this test we calculate the difference between the time series that were observed in the first and third simulations described above. We then divide this by the difference between the first and second time series.

An NPT version of this calculation is performed as well as an NVT calculation if the virial is passed to PLUMED.

Trajectories

  1. Input and output files for the unpeturbed calculation are available in this zip archive

  2. Input and output files for the peturbed calculation are available in this zip archive

  3. Input and output files for the peturbed calculation in which a PLUMED restraint is used to undo the effect of the changed MD parameters are available in this zip archive

Results

Original With PLUMED Effect of peturbation % Difference
-18174.8223 11.6346 -18174.8223 11.6346 0.0000 0.0000 0.0000 0.0000
-18171.8203 11.6346 -18193.2891 11.6346 6.8730 0.0000 312.3615 0.0000
-18194.6055 11.6475 -18234.4980 11.6321 23.4238 0.0054 170.3077 284.9140
-18167.9082 11.6475 -18289.0840 11.6321 21.5430 0.0054 562.4841 284.9140
-18155.9590 11.6475 -18331.0039 11.6321 27.0703 0.0054 646.6306 284.9140
-18139.1270 11.6475 -18356.3047 11.6321 31.0371 0.0054 699.7357 284.9140
-18122.8613 11.6475 -18364.6602 11.6321 34.8945 0.0054 692.9419 284.9140
-18112.9512 11.6475 -18362.0547 11.6321 39.8848 0.0054 624.5580 284.9140
-18112.5176 11.6475 -18356.4590 11.6321 45.8477 0.0054 532.0695 284.9140
-18120.4531 11.6475 -18353.6797 11.6321 51.0352 0.0054 456.9920 284.9140
-18132.0957 11.6475 -18355.4102 11.6321 53.1465 0.0054 420.1867 284.9140
-18142.0840 11.6475 -18360.2207 11.6321 51.2051 0.0054 426.0060 284.9140
-18148.0684 11.6475 -18366.6465 11.6321 47.2441 0.0054 462.6566 284.9140
-18152.7715 11.6475 -18375.5879 11.6321 46.0859 0.0054 483.4803 284.9140
-18162.1055 11.6475 -18389.7168 11.6321 51.9004 0.0054 438.5542 284.9140
-18179.7637 11.6475 -18409.9551 11.6321 63.8027 0.0054 360.7861 284.9140
-18202.8438 11.6475 -18432.1738 11.6321 74.6484 0.0054 307.2135 284.9140
-18222.5000 11.6475 -18448.2148 11.6321 75.1699 0.0054 300.2728 284.9140
-18229.7070 11.6475 -18450.9512 11.6321 61.1211 0.0054 361.9767 284.9140
-18221.0977 11.6475 -18439.2090 11.6321 36.6758 0.0054 594.7012 284.9140

The table below includes some of the results from the calculation. The columns contain:

  1. Time series for the energy and volume that were obtained from the simulation at $T$ K, $x_{md}$.
  2. Time series for the energy and volume that were obtained from the simulation at $\alpha T$ K and in which PLUMED applied a restraint on the energy, $x_{pl}$.
  3. The absolute value of the difference between the time series of energies and volumes that were obtained from the simulations running at $T$ K and $\alpha T$ K, $\vert x_{md}’-x_{md} \vert$. No PLUMED restraints were applied in either of these simulations.
  4. The values of $100\frac{\vert x_{md} - x_{pl}\vert }{ \vert x_{md}’-x_{md} \vert}$.

If the PLUMED interface is working correctly the first two sets of numbers should be identical and the final column should be filled with zeros.

Graphical representation (beta)

A visualization of the table above:
engvir_master